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MACS: A quest for the most massive galaxy clusters in the
universe
H. Ebeling1, A.C. Edge2, J.P. Henry1
Received ; accepted
to appear in the June 1, 2001 issue of ApJ
1Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, Hawaii 96822, USA
2Department of Physics, University of Durham, South Road, Durham DH13LE, UK
http://arXiv.org/abs/astro-ph/0009101v2
– 2 –
ABSTRACT
We describe the design and current status of a new X-ray cluster survey
aimed at the compilation of a statistically complete sample of very X-ray
luminous (and thus, by inference, massive), distant clusters of galaxies. The
primary goal of the MAssive Cluster Survey (MACS) is to increase the number
of known massive clusters at z > 0.3 from a handful to hundreds. Upon
completion of the survey, the MACS cluster sample will greatly improve our
ability to study quantitatively the physical and cosmological parameters driving
cluster evolution at redshifts and luminosities poorly sampled by all existing
surveys.
To achieve these goals we apply an X-ray flux and X-ray hardness-ratio cut
to select distant cluster candidates from the ROSAT Bright Source Catalogue.
Starting from a list of more than 5,000 X-ray sources within the survey
area of 22,735 square degrees we use positional cross-correlations with public
catalogues of Galactic and extragalactic objects, reference to Automated Plate
Measuring Machine (APM) colours, visual inspection of Digitized Sky Survey
images, extensive CCD imaging, and finally spectroscopic observations with the
University of Hawaii’s 2.2m and the Keck 10m telescopes to compile the final
cluster sample.
We discuss in detail the X-ray selection procedure and the resulting selection
function, and present model predictions for the number of distant clusters
expected to emerge from MACS. At the time of this writing the MACS cluster
sample comprises 101 spectroscopically confirmed clusters at 0.3 ≤ z ≤ 0.6;
more than two thirds of these are new discoveries. Our preliminary sample is
already 15 times larger than that of the EMSS in the same redshift and X-ray
luminosity range.
– 3 –
Subject headings: galaxies: clusters: general — galaxies: clusters: — cosmology:
observations — X-rays: general
– 4 –
1. Introduction
The evolution of clusters of galaxies over cosmological timescales is primarily driven
by gravitational processes, such as the initial gravitational collapse of overdense regions
in the primordial universe and their subsequent growth through accretion and cluster
mergers. The formation rate of the final products of this process – relaxed, massive galaxy
clusters – can be modeled straightforwardly for different world models (Press & Schechter
1976). The abundance of clusters as a function of redshift is thus an important diagnostic
of cosmological parameters, primarily the normalized present-day matter density of the
universe, Ω0, and the amplitude of fluctuations in that matter, σ8 (e.g. Oukbir & Blanchard
1997; Eke et al. 1998; Henry 2000).
Although cosmological studies can, in principle, be conducted with poor clusters, their
slow evolution in all models of cluster formation means that very large, statistically well
defined samples at very high redshift (z ∼> 1) are required to obtain significant constraints.
In contrast, observations of the most massive systems, which are rarest and evolve fastest
in all cosmologies, provide tight constraints already at moderate redshift. For instance, the
predicted space density of galaxy clusters with intra-cluster gas temperatures of kT ∼ 7
keV at z ∼ 0.5 is more than a factor of ten higher in a flat or open universe with Ω0 = 0.3
than in a closed universe with Ω0 = 1; at z ∼ 1 the difference approaches two orders of
magnitude (Viana & Liddle 1996; Eke et al. 1996). For yet hotter (i.e., more massive)
clusters the dependance of the formation rate on the chosen world model is even stronger.
As long as all systems are assumed to be virialized, only global cluster properties
(total X-ray luminosity, global gas temperature, total mass) need to be known to constrain
cosmological parameters. Virialization is, however, only one and often an intermittent
state, preceded and, likely, interrupted by periods of growth through mergers, accretion,
and internal relaxation. A statistically complete, large sample of massive, distant clusters
– 5 –
would be invaluable to investigate in detail the physical mechanisms governing these
evolutionary processes for the three main cluster components dark matter, gas, and galaxies.
Such an investigation is, again, most feasible for massive clusters which are – scatter
in the respective relations notwithstanding – likely to be also the most X-ray luminous
and optically richest. They are therefore prime targets for studies of the density and
temperature distribution of the intra-cluster gas as well as of the properties of the cluster
galaxy population. Galaxy clusters also act as powerful gravitational lenses distorting
the images of background galaxies behind the cluster, and create observable changes in
the shape of the spectrum of the cosmic microwave background (CMB) radiation passing
through them (Sunyaev-Zel‘dovich [SZ] effect). Lensing observations and detections of the
SZ effect allow independent measurements of the distribution of dark matter and gas in
clusters, and yet again the observed signal is strongest for massive clusters.
In the local universe (z ∼< 0.3) dozens of massive clusters have been known and studied
in some detail for a long time. What we are still lacking, and what is crucial for evolutionary
studies, is a sizeable sample of the high-redshift counterparts of these well-studied local
systems. In this paper we argue that the required sample of massive, distant clusters is
currently best compiled at X-ray wavelengths, we present an overview of previous X-ray
cluster surveys, and show that the ROSAT All-Sky Survey can be used efficiently to compile
this sample (Section 2). In Section 3 we introduce the MAssive Cluster Survey (MACS),
describe its characteristics and selection function, and discuss predictions for the MACS
sample size based on a no-evolution model. Finally, we present a status report which
demonstrates the efficiency of our approach (Section 4).
We assume h = H0/50 Mpc s km−1 = q0 = 0.5 throughout. Unless explicitly stated
otherwise, all X-ray fluxes and luminosities are quoted in the 0.1–2.4 keV band.
– 6 –
2. X-ray Cluster Surveys
The arguably least biased and most secure way of detecting massive, distant clusters is
through wide-angle radio and sub-mm surveys optimised to detect the Sunyaev-Zel‘dovich
(SZ) effect which is independent of cluster redshift. However, with suitable SZ surveys
remaining infeasible for some time to come, the currently best way to compile statistically
complete cluster samples is through the detection of X-ray emission from the hot
intra-cluster gas. X-ray cluster surveys are unbiased in the sense that they exclusively
select gravitationally bound objects and are essentially unaffected by projection effects
(e.g., van Haarlem, Frenk & White 1997). If complete above a certain limiting X-ray
flux, the resulting statistical cluster samples will have a well-defined selection function (a
simple function of X-ray flux and, sometimes, X-ray extent) that immediately allows the
computation of the effective survey volume for any real or hypothetical cluster. Finally, an
X-ray cluster survey targeting only intrinsically X-ray luminous clusters has the additional
advantage of focusing on systems that are the ones easiest to detect at any given redshift
and for which the impact of contamination from unresolved X-ray point sources is lowest.
Several X-ray flux limited cluster samples have been compiled (and to different degrees
published) in the past decade; an overview of the solid angles and flux limits of these surveys
is presented in Fig. 1. Two kinds of surveys can be distinguished: serendipitous cluster
surveys (Bright SHARC, Romer et al. 2000a; CfA 160 deg2 survey, Vikhlinin et al. 1998a;
EMSS, Gioia et al. 1990a; RDCS, Rosati et al. 1998; SHARC-S, Burke et al. 1997; WARPS,
Jones et al. 1998) and contiguous area surveys (BCS, Ebeling et al. 1998; BCS-E, Ebeling et
al. 2000a; NEP, Henry et al. 2001; RASS-BS, DeGrandi et al. 1999; REFLEX, Guzzo et al.
1999). The former surveys use data from pointed X-ray observations, whereas the latter are
all based on the ROSAT All-Sky Survey (RASS, Trümper et al. 1993). With the exception
of the NEP survey, all contiguous cluster surveys cover close to, or more than, 10,000 square
– 7 –
degrees but are limited to the X-ray brightest clusters. This fundamental difference in
depth and sky coverage has important consequences. As shown in Fig. 1, the NEP survey
as well as all serendipitous cluster surveys (with the possible exception of the EMSS) cover
too small a solid angle to detect a significant number of X-ray luminous clusters (defined as
clusters with LX > 5 × 1044 erg s−1 in the 0.5–2.0 keV band or, equivalently, LX > 8 × 10
44
erg s−1 in the 0.1–2.4 keV band). All previous RASS large-area surveys, on the other hand,
are capable of finding these rarest systems, but are too shallow to detect them in large
numbers at z > 0.3.
The observational situation summarized in Fig. 1 has led to the misconception that
“RASS-based surveys do not have the sensitivity to detect clusters at z > 0.3” (Romer et
al. 2000b). As demonstrated by MACS (see the selection function shown in Fig. 1 and
Section 3), the RASS provides unparalleled areal coverage and sufficient sensitivity to
detect hundreds of X-ray luminous clusters at z ∼> 0.3. Whether such systems actually
exist in large numbers has, however, been the subject of much debate. Based on very small
samples, or in fact non-detections, from serendipitous X-ray cluster surveys (the EMSS and
CfA surveys) two groups have claimed to find strong negative evolution in the abundance
of X-ray luminous clusters already at redshifts of z ∼ 0.35 (Henry et al. 1992, Vikhlinin et
al. 1998b), in conflict with other studies (based on the EMSS and WARPS cluster samples)
that find at best mild evolution at z > 0.5 (Luppino & Gioia 1995; Ebeling et al. 2001). As
we shall show in the following, the ROSAT All-Sky Survey holds the key to resolving this
dispute which has profound implications for our understanding of cluster evolution.
3. The MAssive Cluster Survey (MACS)
MACS was designed to find the population of (possibly) strongly evolving clusters, i.e.,
the most X-ray luminous systems at z > 0.3. By doing so, MACS will re-measure the rate
– 8 –
10 100 1000 10000solid angle (square degrees)
10-14
10-13
10-12
10-11
flux
lim
it [0
.5 -
2.0
keV
] (e
rg c
m-2
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)
all-
sky
10 100 1000 10000solid angle (square degrees)
10-14
10-13
10-12
10-11
flux
lim
it [0
.5 -
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keV
] (e
rg c
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10 cl
uster
s with
L X >
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44 erg s
-1 , any
z
10 X
-ray l
umino
usclus
tersat z >
0.3
100
X-ra
y
lumino
usclu
sters
at z >
0.3
optical detection limit at z ~ 1.3
REFLEX
RASS1-BS
BCS
BCS-E
160 deg2
SHARC-S
RDCS
Bright SHARC EMSS
WARPS
NEP
MACS
Fig. 1.— The selection functions of all major X-ray cluster surveys of the past decade. Also
shown is the solid angle required at a given flux limit to (statistically) detect 10 (or 100) X-ray
luminous cluster at any redshift (or at z > 0.3). Note how, of all previous surveys, only the EMSS,
BCS, and REFLEX projects are just sensitive enough to detect a small number of distant, X-ray
luminous systems.
– 9 –
of evolution and test the results obtained by the EMSS and CfA cluster surveys. Unless
negative evolution is very rapid indeed, MACS will find a sizeable number of these systems
(see Section3.5) and thus provide us with targets for in-depth studies of the physical
mechanisms driving cluster evolution and structure formation.
In this section we give the basic X-ray selection criteria used for MACS, derive the
MACS selection function, and describe the procedure applied to convert detect fluxes
to total cluster fluxes. We then describe the cluster identification procedure and finally
present predictions for the number of clusters expected to emerge from MACS under the
no-evolution assumption.
3.1. X-ray selection criteria
As indicated in Fig. 1, MACS aims to achieve the goals outlined above by combining
the largest solid angle of any RASS cluster survey with the lowest possible X-ray flux limit.
Our survey is based on the list of 18,811 X-ray sources contained in the RASS Bright Source
Catalogue (RASS-BSC, Voges et al. 1999) which has a limiting minimal count rate of 0.05
ct s−1 within the detect cell and in the 0.1–2.4 keV band. Drawing from this list MACS
applies the following X-ray selection criteria:
• |b| ≥ 20◦, −40◦ ≤ δ(J2000) ≤ 80◦ to ensure observability from Mauna Kea; the
resulting geometric solid angle is 22,735 deg2; 11,112 RASS-BSC sources fall within
this region
• X-ray hardness ratio HR greater than HRmin = max[
−0.2,−0.55 + log(
nH1020 cm−2
)]
as derived from the ROSAT Brightest Cluster Sample (Ebeling et al. 1998) with the
additional constraint that HRmin < 0.7; HR is defined as (h − s)/(h + s) where s and
h are the PSPC countrates in the soft (PHA channels 11 to 41) and hard bands (PHA
– 10 –
channels 52 to 201), respectively; 6,750 X-ray sources remain
• fX ≥ 1 × 10−12 erg cm−2 s−1 where fX is the detect cell flux (see Section 3.3) in the
0.1–2.4 keV band; 5,654 RASS-BSC sources remain
• detected net count limit of 17 photons (see Section 3.2); 5504 sources remain
The conversion from net count rate to X-ray flux is performed using Xspec assuming
a standard Raymond-Smith plasma spectrum, a metallicity of 0.3, and a gas temperature
kT of 8 keV; we use the Galactic nH value from Dickey & Lockman (1990) in the direction
of each cluster to account for absorption. The assumed X-ray temperature of 8 keV is
obtained from the LX-kT relation of White, Jones & Forman (1997) for an X-ray luminosity
of 9 × 1044 erg s−1 (0.1–2.4 keV), typical of MACS clusters (see Section 3.3).
We stress that we do not use the X-ray extent provided in the RASS-BSC as a selection
criterion. As shown by Ebeling and co-workers (1998, appendix A) for the BCS (z < 0.3)
this parameter is too unreliable to be used efficiently for the selection of cluster candidates,
to the extent that at least 25% of all real clusters would be missed at any given flux limit
(see also Section 4).
3.2. X-ray selection function
To compute the X-ray selection function, i.e., the effective solid angle of the MACS
survey as a function of X-ray flux, we need to know the cluster detection efficiency and
the depth of the RASS across our study region. The detection algorithm used for the
compilation of the RASS-BSC is optimized for the detection of point sources and is
known to be relatively insensitive to low-surface brightness emission (Ebeling et al. 1998).
While this is a serious problem for the completeness of RASS-based cluster samples at
– 11 –
low redshift, it does not affect MACS which, by design, targets only distant clusters. At
z = 0.3, the limiting redshift of our survey, the canonical value of the cluster core radius
of 250 kpc corresponds to an angular size of 45 arcsec, comparable to the FWHM of the
RASS point-spread function (PSF, Böse 2000). Therefore the detection efficiency of distant
clusters in the RASS will not differ markedly from that of point sources of similar X-ray
flux. Hence, we can derive the effective detection limit using all RASS-BSC sources.
In Fig. 2 we show the histogram of the detected net counts of all RASS-BSC X-ray
sources with exposure times between 200 and 300 seconds. The upper exposure time limit
of 300s was chosen to eliminate artificial distortions at the low-count end of the histogram
due to the presence of lower limits in the RASS-BSC in both count rate and net counts
of 0.05 ct s−1 and 15 photons, respectively. An additional, lower limit of 200s in exposure
time was applied to create a relatively narrow range of exposure times, thus ensuring that
a complete sample can be described by a single power law3. Figure 2 shows that, although
the RASS-BSC contains sources with as few as 15 counts (as stated in Voges et al. 1999),
the catalogue is not complete to this limit. Based on a comparison with the best-fitting
power law we adopt instead a value of 17 net counts as the completeness limit.
Combining the net count limit of 17 photons with the RASS exposure map (Fig. 3)
yields the count rate selection function, i.e., the fractional MACS survey area for which the
RASS-BSC could be complete at a given count rate. In practice, the count rate cut at 0.05
ct s−1 imposed on the RASS-BSC source list truncates this function as shown in Fig. 4.
Conversion from count rate to X-ray flux as detailed in Section 3.1 transforms the count
rate selection function into the desired X-ray flux selection function. As shown in Fig. 5,
3We stress that these exposure time cuts are applied only here to establish the net count
limit of completeness for the RASS-BSC; they are not applied to the X-ray source list MACS
is compiled from.
– 12 –
10 100BSC net source counts
10
100
n
10 100
10
100
Fig. 2.— The distribution of net detected counts for all RASS-BSC sources with exposure times
between 200 and 300 seconds. The dashed line shows the best power-law fit to the data; the dotted
line marks the completeness limit at 17 counts adopted by us.
– 13 –
and as expected from the soft energy passband of the ROSAT PSPC, the selection function
is not sensitive to variations in the assumed X-ray temperature from 6 to 10 keV.
Based on the MACS selection function we divide the X-ray source list compiled by
applying the criteria listed in Section 3.1 into an X-ray bright subset (fX ≥ 2 × 10−12 erg
cm−2 s−1) and an X-ray faint extension (fX = 1 − 2 × 10−12 erg cm−2 s−1). The bright
subsample is complete over 93% of the geometric solid angle of our survey; when combined
with the faint extension the effective search area decreases to 59% of the maximal survey
area of 22,735 deg2.
3.3. Flux corrections
The X-ray fluxes derived from the RASS-BSC count rates as detailed above are detect
fluxes, i.e., they correspond to the emission detected by the RASS-BSC detection algorithm
within a specific circular aperture. The radius of this detect cell aperture depends on the
apparent X-ray extent of the source and ranges from 5 arcmin (the default value) to a
maximal value of 16.5 arcmin.
To convert detect fluxes into total cluster fluxes we assume that the intrinsic X-ray
surface brightness profile follows a beta model, I ∝ (1 + r2/r2c)−3β+0.5 (Cavaliere &
Fusco-Femiano 1976), with β = 2/3 and core radius rc = 250 kpc. We then convolve this
spatial emission model with the RASS PSF (Böse 2000) and compute the fraction of the
observable emission that falls within a set of circular apertures of 5, 6, 7.5, 10, and 15
arcmin radius. The resulting range of flux correction factors is shown in Fig. 6. Within the
MACS redshift range the flux correction factor is not a strong function of redshift; it does
depend, however, strongly on the size of the extraction aperture and, at least for the smaller
apertures, on the assumed value of rc. While the extraction radius is known for each cluster,
– 14 –
Fig. 3.— RASS exposure map (Aitoff projection) in celestial coordinates (http://www.xray.mpe.
mpg.de/rosat/survey/rass-3/sup/nx.fits.gz). The solid white lines delineate the MACS survey area;
the dashed black lines mark the excluded 40 degree wide band centred on the Galactic equator.
The highest exposure time of several ten thousand seconds is reached at the north ecliptic pole,
the median exposure time within the MACS survey area is 360 seconds.
http://www.xray.mpe
– 15 –
0.01 0.10RBS count rate (s−1)
0.0
0.2
0.4
0.6
0.8
1.0
frac
tion
of M
AC
S so
lid a
ngle
Fig. 4.— The MACS count rate selection function corresponding to a count limit of completeness
of 17 net photons in the detection aperture. The solid line shows the fraction of the MACS search
area for which the RASS-BSC would be complete if no count rate limit were applied. The dashed
line marks where the count rate limit of 0.05 ct s−1 of the RASS-BSC truncates the selection
function.
– 16 –
1MACS flux limit (10−12 erg cm−2 s−1)
0
5000
10000
15000
20000
solid
ang
le (
deg2 )
1MACS flux limit (10−12 erg cm−2 s−1)
0
5000
10000
15000
20000
solid
ang
le (
deg2 )
0.5 3 50.0
0.2
0.4
0.6
0.8
1.0
frac
tion
of to
tal s
olid
ang
leFig. 5.— The MACS selection function: solid angle covered as a function of detected X-ray flux in
the 0.1–2.4 keV band. The dashed line shows the selection function attainable if no count rate limit
had been applied to the RASS-BSC. The solid lines show the effective MACS selection function
with the count rate limit applied and assuming cluster gas temperatures of 6, 8, and 10 keV. The
dotted lines mark the detect cell flux limits, and corresponding sky coverages, of the bright and
faint MACS subsamples.
– 17 –
the core radius is not. Next to the Poisson error of the number of directly detected photons,
the variation of the correction factor with core radius is the second largest contributor to
the uncertainty in the total X-ray fluxes and luminosities of MACS clusters.
While the extraction radius associated with detections of nearby clusters (z < 0.1)
is often greater than the default value (25% of the nearby clusters feature values greater
than five arcmin), large extraction radii become rare as the angular extent of the cluster
emission decreases with increasing cluster redshift. At z > 0.3, the MACS redshift range,
the nominal aperture size of five arcmin radius is used for more than 97% of all clusters.
Using the flux correction factor for this default extraction radius and assuming rc = 250
kpc we derive limiting (minimal) total cluster luminosities of 4.7 and 9.5 × 1044 erg s−1 for
the faint and bright MACS subsamples at z > 0.3; at z > 0.4 the two subsamples contain
only clusters with luminosities in excess of 8.1 and 16.3 × 1044 erg s−1, respectively.
3.4. Cluster identification
The cluster identification procedure adopted for MACS involves five steps:
1. Cross-correlation of the list of 5504 RASS-BSC sources with all objects in the
SIMBAD and NED databases. Possible counterparts of an X-ray source are extracted
within a search radius of 1 arcmin (stars, galaxies, active galactic nuclei [AGN],
QSOs) or 3 arcmin (supernova remnant [SNRs], galaxy clusters). These search radii
are consistent with the 3σ uncertainty of the RASS-BSC source positions of 1 arcmin
(98% limit of error distribution) for point sources and 2 arcmin (98% limit) for
extended sources, and account for an additional uncertainty of about 1 arcmin in the
positions of catalogued supernova remnants and clusters of galaxies.
2. Visual inspection of Digitized Sky Survey (DSS) images (second generation where
– 18 –
0.20 0.30 0.40 0.50 0.60 0.70 0.80redshift z
1.00
1.10
1.20
1.30
1.40
flux
corr
ectio
n fa
ctor
0.20 0.30 0.40 0.50 0.60 0.70 0.801.00
1.10
1.20
1.30
1.40
15
10
7.5
6
5
Fig. 6.— Flux correction factors to convert from detect flux to total cluster flux. The solid lines
show the redshift dependence of the correction factor for various extraction apertures with radii
(in arcmin) as labeled. For the smallest and the largest aperture the shaded regions indicate the
dependence of the flux correction factor on the assumed value of the core radius of the emission
profile (varied from 200 to 300 kpc).
– 19 –
available). The size of these images is 5 × 5 arcmin2 corresponding to at least
1.65 × 1.65 Mpc2 within the redshift range of our survey (z > 0.3).
3. Search for extremely blue (O−E < 1.3) or red (O−E > 2) counterparts in the APM
(Automated Plate Measuring machine; Irwin, Maddox & McMahon 1994) object
catalogue to tentatively identify stars, AGN, and BLLac objects. Only objects within
25” of the RASS-BSC X-ray position are considered. The quoted colour and angular
separation thresholds correspond to 95% confidence limits for identifications with
these types of objects obtained from cross-correlations of the APM catalogue with
known AGN and stars.
4. CCD imaging in the R (bright source list) or I band (faint source list) of all X-ray
sources without (or with ambiguous) identifications as well as of all possibly distant
(z ∼> 0.2) cluster candidates with the University of Hawaii’s 2.2m telescope. At
exposure times of 3 × 2 min in R and 3 × 3 min in I these imaging observations are
deep enough to unambiguously detect rich clusters out to z ∼ 0.84
5. Spectroscopic observations with the UH2.2m and Keck 10m telescopes of all confirmed
clusters with estimated redshifts of z ∼> 0.2.
For an RASS-BSC source to be flagged as a non-cluster before CCD images are
obtained, the cross-correlation with Galactic and extragalactic object catalogues has to
4 The WARPS team discovered the rich clusters ClJ0152.7−1357 (z = 0.833, Ebeling et
al. 2000b) and ClJ1226.9+3332 (z = 0.888, Ebeling et al. 2001) in the first of three 4 min
I band exposures taken with the same instrumentation at the UH2.2m telescope as is used
by us for MACS. The mentioned two WARPS clusters constitute a complete sample at this
redshift.
– 20 –
yield an unambiguous non-cluster identification that is supported by the appearance of the
field in the DSS finders, as well as by the APM colour (where available) of the counterpart.
Typical examples of such obvious identifications are bright stars and nearby galaxies (with
and without nuclear activity). We stress that DSS finders are obtained and examined for
all RASS-BSC sources meeting the initial X-ray selection criteria (Section 3.1), and that we
do proceed to CCD imaging in spite of the presence of a listed non-cluster counterpart if,
for instance, a catalogued QSO is not clearly visible in the DSS image or if, in addition to
the QSO, an overdensity of faint objects is apparent in our finders.
Unless a RASS-BSC source has been firmly identified as a non-cluster, or as a cluster
at z < 0.2 (where z can be a measured or estimated redshift), CCD images of the source
over a 7.5 × 7.5 arcmin2 field-of-view are obtained with the University of Hawaii’s 2.2m
telescope. Since MACS clusters, in contrast to the majority of the systems detected in
serendipitous cluster surveys, are by design and without exception very X-ray luminous
(Section 3.3) they are usually also optically rich and thus obvious even in shallow CCD
images. All distant clusters (zest > 0.2) confirmed by imaging observations are subsequently
targeted in spectroscopic observations where we obtain redshifts of at least two cluster
members, one of them the apparent brightest cluster member.
A systematic effect that is difficult to quantify is the impact of X-ray contamination
on our sample. We cannot rule out that we may have included a small number of clusters
at z > 0.3 that are significantly contaminated by X-ray point sources and would fall
below our flux limit if the non-diffuse emission were subtracted. We attempt to identify
possibly contaminated clusters by obtaining deeper (3 × 4 min) optical images in each of
three passbands (V, R, I) of all MACS clusters with spectroscopic redshifts of z > 0.3.
Fig. 7 shows such a colour image (of a newly discovered MACS cluster at z = 0.453) and
illustrates how the optical richness of MACS clusters allows an unambiguous identification
– 21 –
already from relatively shallow CCD images. A (by MACS standards) low optical richness
of a system in these colour images is one possible indicator of contamination, as is the
presence of unusually red or blue objects close to the X-ray position. In future follow-up
work we shall attempt to obtain spectra of potential contaminants identified in this manner.
However, ultimately we will be not be able to quantify the level of X-ray contamination
until deeper pointed X-ray observations of all MACS clusters have been performed.
While we believe to have taken all feasible precautions against missing distant clusters,
the above procedure (or any other) can never be failsafe. Albeit unlikely, a distant
cluster might be obscured by a bright star which we accepted as the X-ray counterpart.
Alternatively, a very distant cluster which is not visible on the DSS finder can be missed if an
acceptable optical counterpart to the X-ray source is present in the foreground (catalogued
AGN or QSO at lower redshift). While, in both of these examples, the eventually accepted
identification is likely to contribute to the observed X-ray emission, we can not rigorously
rule out that we have missed a small number of distant clusters above our X-ray flux limit.
As for all cluster surveys, the size of the cluster sample emerging from MACS, as well as all
volume-normalized quantities derived from it, should thus be considered to represent lower
limits.
3.5. No-evolution prediction
A prediction for the size of the final MACS sample under the no-evolution assumption
can be obtained by folding the local cluster X-ray luminosity function (XLF) as measured
from the ROSAT Brightest Cluster Sample (Ebeling et al. 1997) through the MACS
selection function shown in Fig. 5. In this process, we use our usual assumptions to convert
from X-ray luminosity to flux and from total cluster flux to detect cell flux (see Sections 3.1
and 3.3) and integrate the cluster XLF out to z = 1.
– 22 –
Fig. 7.— Colour image (5×5 arcmin2) of a newly discovered MACS cluster at z = 0.453, based on
3× 4min exposures in each of the V, R and I bands with the University of Hawaii’s 2.2m telescope.
The RASS-BSC X-ray position is 30” south of the image center. We obtain images like this one
for all MACS clusters with spectroscopic redshifts of z > 0.3 to allow the optical richness of these
systems to be assessed, to efficiently select cluster galaxies for multi-object spectroscopy, and to
identify unusually red or blue objects that might be X-ray contaminants.
– 23 –
The resulting model prediction is shown in Fig. 8. Although the uncertainties
introduced by the errors in the Schechter function parameterization of the local XLF
(z < 0.3) are considerable, it is safe to say that about 300 clusters are expected to emerge
from MACS if there is no evolution in the cluster XLF out to z = 1. Only at z > 0.7 would
the number of MACS clusters approach or fall below about ten, thus entering the Poisson
regime.
These numbers are sufficiently high for us to be confident that MACS will produce not
only the largest sample of massive, distant clusters compiled to date (a relative statement),
but also a sizeable one in absolute terms, even in the presence of strong negative evolution.
4. MACS: Status as of December 2000
As part of the procedure described in detail in Section 3.4 we have, so far, obtained 349
CCD images of MACS cluster candidates and measured redshifts for 131 clusters confirmed
by the imaging observations. As of December 2000, we have identified more than 850
clusters of galaxies at all redshifts; Fig. 9 shows the redshift distribution of the 787 systems
with spectroscopic redshifts. As a by-product, MACS has thus already delivered by far the
largest X-ray selected cluster catalogue to emerge from the RASS to date.
The redshift distribution shown in Fig. 9 is skewed toward high redshifts because
our spectroscopic follow-up observations target exclusively systems with zest > 0.2. Up to
December 2000 101 clusters were found to have z > 0.3; a further 37 clusters confirmed in
imaging observations and with zest > 0.2 still await spectroscopic confirmation. Of the 101
clusters in the preliminary MACS sample only 29 were previously known. These 29 hail
from a wide variety of projects, including the optically selected GHO sample (Gunn, Hoessel
& Oke 1986), the Abell catalogue (Abell, Corwin & Olowin 1989) and the X-ray selected
– 24 –
0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00redshift z
1
10
100
num
ber
(>z)
0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00redshift z
1
10
100
num
ber
(>z)
Fig. 8.— Number of clusters above redshift z predicted to emerge from MACS under the no-
evolution assumption. We use the local cluster X-ray luminosity function (XLF) from the BCS
(Ebeling et al. 1997). The uncertainty in the prediction indroduced by the errors in the Schechter
function parameterization of the BCS XLF is represented by the dark shading; the light shading
shows the additional effect of varying the core radius between 200 and 300 kpc. As shown by the
dotted lines, of the order of ten clusters at z > 0.7 are expected if the XLF does not evolve out to
z = 1.
– 25 –
EMSS5 (Gioia & Luppino 1994) and BCS (Ebeling et al. 1998, 2000) cluster samples.
Figure 10 shows the X-ray luminosity–redshift distribution of our preliminary sample
at z > 0.3, compared to the one for the BCS at z < 0.3, and the one for the EMSS at
0.3 < z < 0.6. Note how MACS extends the redshift baseline for studies of the most
X-ray luminous clusters (LX ∼ 1 × 1045 erg s−1) from z ∼< 0.3 to z ∼< 0.6, and how MACS
clusters are, in general, much more X-ray luminous than EMSS clusters. In fact only six
EMSS clusters come close to the X-ray luminosities sampled by MACS at z > 0.3; four
of these are rediscovered by us (MS2137.3−2353, MS1358.4+6245, MS0451.6−0305, and
MS0015.9+1609), the other two (MS0353.6−3642 and MS1008.1−1224) lie just below
our flux limit. MACS thus contains already more than 15 times more clusters in this
cosmologically most important region of the LX-z plane than the EMSS, providing us for
the first time with a sizeable and statistically robust sample for studies of the properties of
the high-redshift counterparts of the most massive local clusters.
We emphasize again that the completeness of this sample, compiled from RASS
data, hinges critically upon our ignoring the RASS-BSC extent parameter. As shown in
Fig. 11 34% of all MACS clusters at z > 0.3 are classified as X-ray point sources by the
RASS-BSC detection algorithm. Based on a comparison of the extent values assigned by
the RASS-BSC algorithm to detections of Abell clusters and to a control set of random
RASS sources, Ebeling and coworkers (1993) find that extent values below 35 arcsec are in
general spurious. If this threshold value had been adopted for MACS, our survey would
have missed more than half of the 101 clusters in our preliminary sample.
5The less than a handful EMSS clusters rediscovered by MACS constitute the largest
statistically complete previous cluster sample in this redshift and X-ray luminosity range.
– 26 –
0.00 0.10 0.20 0.30 0.40 0.50 0.600
20
40
60
80
100
0.00 0.10 0.20 0.30 0.40 0.50 0.60redshift z
0
20
40
60
80
100
num
ber
of c
lust
ers total: 787
z > 0.3: 101
Fig. 9.— The redshift distribution of the 787 clusters identified in the MACS project to date.
The 101 clusters at z > 0.3 that form the preliminary MACS sample are highlighted. All clusters
have spectroscopic redshifts.
– 27 –
0.00 0.10 0.20 0.30 0.40 0.50 0.60redshift z
0.1
1.0
10.0
100.0
LX (
1044
erg
s−1 ,
0.1
− 2
.4 k
eV)
eBCS MACS(as of December 2000)
EMSS
Fig. 10.— The luminosity–redshift distribution of the extended BCS (Ebeling et al. 1998, 2000)
at z < 0.3 and of the preliminary MACS sample (101 clusters) at z > 0.3. Also plotted (open
circles) are the loci of the 23 EMSS clusters at 0.3 < z < 0.6 (Henry et al. 1992). The solid line
marks the flux limits of the BCS and MACS surveys; the dashed line shows the flux limit of the
X-ray bright MACS subsample. By design MACS finds the high-redshift counterparts of the most
X-ray luminous (and best studied) clusters in the local universe.
– 28 –
0 20 40 60 80 100RBS extent (arcsec)
0.0
0.2
0.4
0.6
0.8
1.0
N(>
exte
nt)
Fig. 11.— The cumulative RASS-BSC extent distribution of the 101 MACS clusters in our
preliminary sample. The dashed lines mark the extent threshold of 35 arcsec above which a source
can be considered to be genuinely extended according to Ebeling et al. (1993), and the completeness
(44%) of the MACS sample that would have resulted if this extent threshold had been used as an
X-ray selection criterion.
– 29 –
5. Summary
We describe the design and status of the MAssive Cluster Survey (MACS), the first
X-ray cluster survey aimed at the compilation of a large, statistically complete sample of
exclusively X-ray luminous (LX ∼> 5 × 1044 erg s−1, 0.1–2.4 keV), distant (z > 0.3) clusters.
The systems targeted by our survey are the rarest, most massive clusters whose evolution
places the tightest constraints on the physical and cosmological parameters of structure
formation on cluster scales.
Based on the ROSAT Bright Source Catalogue of RASS detections, MACS uses the
spectral hardness of the X-ray emission and the X-ray flux in the detect aperture to
select 5504 X-ray sources in a search area of 22,735 deg2. A comprehensive identification
programme has so far led to the discovery of more than 800 clusters at all redshifts; imaging
and spectroscopic follow-up observations have confirmed 101 clusters at z > 0.3. MACS has
thus already more than tripled the number of massive, distant clusters known; compared to
the EMSS sample our current preliminary sample represents an improvement in size of a
factor of 15 in the MACS redshift and luminosity range.
Under the no-evolution assumption, MACS is expected to uncover up to, and perhaps
more than, 300 clusters at z > 0.3. However, if evolution is strong and negative, the total
sample could comprise as few as as 100 clusters. In any case MACS will increase greatly
the number of distant, massive clusters known and, hopefully, lead to similarly impressive
improvements in our understanding of the properties and evolution of these most massive
collapsed entities in the universe.
We thank the telescope time allocation committee of the University of Hawai‘i for their
generous support of the MACS optical follow-up program. HE gratefully acknowledges
financial support from NASA LTSA grant NAG 5-8253. ACE thanks the Royal Society
– 30 –
for financial support. This research has made use of the NASA/IPAC Extragalactic
Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of
Technology, under contract with the National Aeronautics and Space Administration. The
Digitized Sky Surveys were produced at the Space Telescope Science Institute under US
Government grant NAG W-2166. The images of these surveys are based on photographic
data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK
Schmidt Telescope.
– 31 –
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This manuscript was prepared with the AAS LATEX macros v4.0.
